First slide

Spherical refracting surface's

Question

A point object is placed at the center of a glass sphere of radius 6 cm and refractive index 1.5. The distance of the virtual image from the surface of the sphere is

Moderate

A

2 cm
B

4 cm
C

6 cm
D

12 cm

Solution

$Using refraction formula \frac{_{1} μ_{2} - 1}{R} = \frac{_{1} μ_{2}}{v} - \frac{1}{u} in given case, medium (1) is glass and (2) is air$
$So \frac{{gμ}_{a} - 1}{R} = \frac{{gμ}_{a}}{v} - \frac{1}{u} \Rightarrow \frac{\frac{1}{1 .5} - 1}{- 6} = \frac{1}{1 .5 v} - \frac{1}{- 6} \Rightarrow \frac{1 - 1 .5}{- 6} = \frac{1}{v} + \frac{1 .5}{6} \Rightarrow \frac{0 .5}{6} = \frac{1}{v} + \frac{1}{4} \Rightarrow \frac{1}{v} = \frac{1}{12} - \frac{1}{4} = - \frac{2}{12} = - \frac{1}{6} \Rightarrow v = - 6 cm$
II method:
$\frac{μ_{2} - μ_{1}}{R} = \frac{μ_{2}}{v} - \frac{μ_{1}}{u} \frac{1}{2 R} = \frac{1}{v} - \frac{3}{- 2 R} v = - R = - 6 cm$

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